To knock it out solo, what to do is grappel into your bord, whistle for it to attack the quetzel, then whistle stop while you are near it and shoot it. Repeat the process and it should go down. With people, one person can pick you up with a pteranodon and fly to it. You can shoot at the quetzal while your buddy flys ahead of the quetz.
The fun way is to jump off and grapple to your argie and whistle it to attack and since argies are slow it won’t catch up in time so tranq till it goes out also bring parachutes and consider liking so more people will know
If you drop a quetzal due to knockout, and it lands next to a giga...just know, the quetzal belong to the giga. Now you get to watch your would be quetzal get eaten by a giga. Now you can go home and cry.
If you manage to knock a quetzal out, try starve taming. If you never tried starve taming it’s just leaving a Dino’s hunger go to half way or lower and then you start feeding. I’ve done this many times and it’s very useful taming trick.